Supercavitating hydrofoils



Nov. 27, 1962 Filed Dec. 24, 1959 M. P. TULlN SUPERCAVITATING HYDROFOILS 2 Sheets-Sheet 1 0.6 0. 7 0 8 9 I. 0 lNVENTOR BY MW, 42%;;

ATTORNEYS Nov. 27, 1962 M. P. TULlN 3,055,723

SUPERCAVITATING HYDROFOILS Filed Dec. 24, 1959 2 Sheets-Sheet 2 mVENTOR flies/M1 4 P 704 //v ATTORNEYS Free 3,'.t65,. 23 SUPERCAVKTATENG HYDRUFOHLS Marshall l Tulin, Silver Spring, Md. Filed Dec. 24, 1959, Ser. No. 861,846 Qlaims. (tCl. lid-e65) The invention described herein may be used by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefor.

This application is a continuation-in-part of application Serial No. 784,406, filed December 31, 1958, now abandoned.

The present invention relates to hydrofoil structures, and particularly to such structures intended to operate efficiently under supercavitating conditions whether naturally or artificially induced.

These structures can be lift-producing hydrofoils as. for example, the foils of a high speed hydrofoil boat; the blades of a marine propeller; the blades of a fluid pump or turbine; or the working elements of other hydrodynamic machines.

' Cavitating and supercavitating flows are well known phenomena. A cavitating flow is naturally produced in a liquid when the relative speed between an immersed body and the liquid itself is great enough to induce sufficiently low pressures that the liquid is caused to vaporize, thus producing a vapor filled attached cavity. A cavitating flow can also be produced through the artificial introduction of a gas, e.g., air, into the fluid in the vicinity of the immersed body, such that an attached cavity is formed and maintained in the flow. A supercavitating flow dif fers from a conventional cavitating flow in that the gas filled cavity is of sufiicient length as to extend downstream of the body, i.e., it collapses or closes downstream of the body.

Both cavitation and supercavitation have generally caused a loss in the efficiency of a hydrofoil. Further, cavitation, as distinguished from supercavitation, leads to erosion of the surface along which the cavitation occurs and can cause severe vibrations of the hydrofoil structure itself. These effects are a consequence of the closure or collapse of a cavity or cavities on or near the hydrofoil structure rather than downstream thereof.

Cavitation can be avoided, but only by limiting the speed of operation of the hydrofoil structure. For example, one of the facts that has heretofore limited the speeds of ships has been the inability of the conventional marine propeller to operate at high speeds without the occurrence of cavitation and the accompanying adverse effects noted heretofore. The speed at which cavitation occurs in a hydrodynamic device employing rotating hydrofoil blades can be extended by using larger and more slowly rotating blades. However, this technique also soon reaches a practical limit. For example, the reduction gears required to drive the slower ship propellers from high stream or gas turbines are large and expensive, requiring considerable maintenance, and take up space and weight that could be used to greater advantage for other purposes aboard ship.

My invention overcomes the foregoing problems resulting'from cavitation. A lifting hydrofoil has been produced capable of efficiently operating under supercavitating conditions and thereby avoiding mechanical damage to and vibration of, said hydrofoil.

It should be stressed that supercavitating operation has previously been avoided despite the fact that erosion and vibration can be eliminated. Heretofore, supercavitation had drastically affected the efficiency of the hydrofoil because a redistribution of pressures occurred thereon as to adversely alter such efiiciency, to wit, lift to drag ratio of the hydrofoil. When supercavitation occurred, pressures on the foil were distinctly different than when the foil operated without cavitation. As a consequence, a drag always occurred on a foil when it was operating in a supercavitating condition.

By my invention, I have achieved a hydrofoil structure capable of operating under supercavitating conditions, yet without any accompanying adverse effect on the lift to drag ratio. As will be more fully explained hereinafter, I have succeeded in producing a supercavitating hydrofoil whereby, under normal operating conditions, the relative pressures are so compensated as to produce on the forward part of the lower surface of the hydrofoil, a net force in a direction opposite the direction of flow of the fluid relative to the hydrofoil tending to compensate the pressure force on the after part of said lower surface, which acts in the direction of the fluid flow. This, quite simply, tends to maximize the efficiency of the hydrofoil. The result is a hydrofoil which operates under supercavitating conditions to virtually eliminate erosion and vibration, yet with no accompanying adverse effect on the all important lift to drag ratio.

With the above in mind, the primary object of the pres ent invention is to provide a hydrofoil structure capable of operating under either naturally or artificially induced supercavitating conditions with no significant decrease of efiiciency.

Another object of this invention is to provide a supercavitating hydrofoil which is not limited in speed of operation relative to the fluid in which it is immersed.

A further object of my invention is to provide a hydrofoil capable of efficient use in supercavitating propellers.

An additional object of the invention is to provide a hydrofoil which may be used on various structures such as hydrofoil boats, hydrofoil equipped seat planes, fluid turbines and pumps.

A more specific object of my invention is to provide a hydrofoil for operation under supercavitating conditions comprising an upper surface, a lower surface, a sharp leading edge and a trailing edge both formed by the intersection of said upper and lower surfaces, said upper surface shaped so that in normal operation it is entirely within a cavitation envelope and said lower surface is entirely wetted as to eliminate erosion and vibration of the hydrofoil, and said lower surface being so shaped as to maximize the lift to drag ratio.

A more specific object of my invention is to provide a hydrofoil for efficient operation under supercavitating conditions comprising an upper surface, a lower surface, a sharp leading edge and a trailing edge both formed by the intersection of said upper and lower surfaces, said upper surface shaped so that in normal operation it is entirely within a cavitation envelope extending from said leading edge, and said lower surface being (a) entirely wetted in normal operation, (b) esentially of a curvature from the leading edge to the trailing edge following the general geometric equation y"(x)0, wherein x is a value from 0 to s and signifies the distance from the leading edge to a point lying on and measured along a base line drawn through the leading edge and parallel to the direction of the movement of the fluid relative to the hydrofoil, s is the distance from the leading edge to the intersection of the normal projection of the trailing edge on said base line, and y is the normal distance from the said base line to the said lower surface measured positive upwards, and (c) of a concave curvature at the trailing edge, the said lower surface thereby being so shaped as to in normal operation produce on the forward part thereof a net force in a direction opposite the direction of flow of the fluid relative to the hydrofoil which tends to compensate the pressure force on the after part of said lower surface in the direction of the fluid flow, thus maximizing the efliciency of said hydrofoil.

Further objects of the invention will be apparent from the following description and the drawings wherein:

FTGURE 1 shows a cross section of a conventional supercavitating hydrofoil taken along a surface parallel to the direction of relative motion of the fluid, and having a lower surface of a configuration falling outside the scope of my invention, it being understood that such relative motion may be caused by the motion of fluid past a stationary foil, by the motion of the foil in fluid which is at rest far from the foil, or by the combined motions of the foil and the fluid.

FIGURE 2 shows a cross section of a supercavitating hydrofoil contemplating one modification of my invention and taken along a surface parallel to the direction of relative motion of the fluid, the foregoing comments relating to relative motion being equally applicable hereto.

FIGURE 3 is a chart from which the shape of the hydrofoil of FIGURE 2 may be plotted.

FIGURE 4 is a chart showing the lift-drag ratio versus coefficient of lift for the hydrofoils of FiGURES 1 and 2,

respectively; and

FIGURE 5 is a drawing of a blade of a propeller embodying the hydrofoil of FIGURE 2.

Referring to the drawings, FIGURE 1 illustrates a cross section ii, of a conventional supercavitating hydrofoil. This particular hydrofoil has a flat lower surface 3 and a convex upper surface 5. The upper and lower surfaces meet at a sharp leading edge 7 and the trailing edge 9. The arrow 11 represents direction of flow of the fluid relative to the foil. Under normal operating conditions the upper surface 5 is completely enclosed within a cavitation envelope which is generally shown by dashed line 13.

FIGURE 2 shows a cross section of a foil shape 15 constituting one modification of the present invention. This foil has a curved lower surface 17 following the general geometric equation y(x)0, wherein x is of a value from 0 to s and signifies the distance from the leading edge to a point lying on and measured along a base line drawn through the leading edge and parallel to the direction of the movement of the fluid relative to the hydrofoil, s is the distance from the leading edge to the intersection of the normal projection of the trailing edge on said base line, and y is the normal distance from the said base line to the said lower surface measured positive upwards. The upper surface is shown at 19.

The upper and lower surfaces in FIGURE 2 meet at a sharp leading edge 21. The trailing edge is likewise formed by intersection of the upper and lower surfaces at 23. The arrow represents the direction of flow of the fluid relative to the foil. Under normal operating conditions the lower surface 17 is entirely wetted and the upper surface 19 is completely enclosed within a cavitation envelope which originates at the leading edge 21 and extends beyond the trailing edge 23. The general outline of the cavitation is shown by dashed line 27.

The configuration of the foil shown in FIGURE 2 is charted in FIGURE 3. As previously noted, the general geometric equation for the lower surface is y"(x) 0. The specific equation for the family of foils in which the illustrated modification belongs is:

re W- en s 51r s 3 s 4 s where:

x=the coordinate of the foil surface parallel to the direction of the movement of the fluid relative to the foil.

y =the coordinate of the foil surface normal to the x direction.

s=the body chord length of the foil. C =the lift coeificient of the foil defined as 2 pUs where:

This equation for the nondimensional ordinates of the bottom,

yields the curve plotted in FIGURE 3.

The foil shape illustrated in FIGURES 2 and 3 has undergone extensive testing and actual use, particularly as incorporated in marine propellers. At the same time, analogous conventional supercavitating hydrofoils were subjected to comparative test procedures thereby illustrating the relatively high efliciency obtained by my invention.

FIGURE 4 is a graphic comparison of the lift-drag ratio versus coeflicient of lift for the hydrofoils of FIG- URES l and 2, respectively. Curve 29 shows the best lift-drag ratios obtainable by the flat blade hydrofoil of FIGURE 1. A comparison of curve 29 with curve 31, which shows analogous lift-drag ratio for the hydrofoil of FIGURE 2, establishes an efiiciency over six times greater for the latter.

This outstanding increase of efficiency of my hydrofoil over conventional supercavitating hydrofoils can be explained as follows:

When a foil section or hydrofoil is operated at such high speeds that cavitation occurs around the foil, then a redistribution of pressure occurs thereon as to alter the liftdrag ratio. At the time cavitation becomes so wide spread as to reach a supercavitating condition, the pressures on the foil are distinctly different from the case when the foil operates without cavitation. As a consequence, a drag always has occurred on a supercavitating hydrofoil thereby adversely affecting efficiency as noted heretofore.

After extensive investigation, it was determined that drag on a supercavitating hydrofoil can be minimized if the foil shape is so designed as to, in normal operation, (a) provide that the upper surface thereof remains entirely within the cavitation envelope; (b) provide that the lower surface thereof remains entirely wetted; and (c) contemplate a curvature (referring to FIGURE 2) for the lower surface 17 as to produce on the forward part thereof a net force in a direction opposite the direction of flow of the fluid relative to the hydrofoil, which tends to compensate the pressure force on the after part of said lower surface in the direction of the fluid flow, thereby tending to maximize the efficiency of the hydrofoil. These three features meet the basic criteria that are involved in achieving high efliciencies under supercavitating conditions.

Specifically, the upper surface of my hydrofoils must remain entirely within the cavitation envelope in order to minimize friction drag. If the upper surface became wetted, friction drag would be increased through contact between the foil surface and the water, thus, adversely affecting efficiency.

The lower surface must remain entirely wetted, i.e., cavitation must be avoided. Cavitation on the lower surface requires energy and would thereby cause additional drag.

The third criterion involving compensation of pressure forces on the lower surface of my hydrofoil structure is based on the realization that conventional supercavitating hydrofoils possess a significant pressure drag on the lower surface thereof. Specifically, high pressures which exist on the lower surface of a supercavitating hydrofoil and spear/es produce the lift thereon, also act generally rearwardly on such lower surface to produce pressure drag.

With the above in mind, and as noted heretofore, the lower surface of the hydrofoil of the present invention has been so shaped that such pressure drag is minimized. This is achieved by so shaping the lower surface as to produce a compensating force on the forward part thereof, acting opposite to the direction of normal pressure drag and thereby minimizing the net pressure drag component that remains. l have found that a lower surface of concave curvature at the trailing edge and following the general geometric equation y(x)0, wherein x is a value from to s and signifies the distance from the leading edge of the hydrofoil to a point lying on and measured along a base line drawn through the leading edge and parallel to the direction of the movement of the luid relative to the hydrofoil, s is the distance from the leading edge to the intersection of the normal projection of the trailing edge on said base line; and wherein y is the normal distance from the said base line to the said lower surface measured positive upwards, produces this desired result.

Specifically, l have mathematically shown that the pressure drag of supercavitating hydrofoils depends on the distance back from the leading edge of the foil to the center of pressure (the latter is a well known hydrodynamic term being the point upon which acts the sum of all pressures on the foil). With this in mind, I designed the lower surface of a hydrofoil in accordance with the foregoing, to move the said center of pressure further back from the leading edge of the hydrofoil thereby introducing a compensating pressure acting on the forward part of said foil to yield a minimized pressure drag component.

FIGURE shows a single blade 33 and cylindrical hub 35 of a typical marine propeller constructed in accordance with the present invention. It will be understood, however, that such a propeller will normally have two or more blades. Blade 33 has a sharp leading edge 37 and a trailing edge 39 which together define a front surface 41 and a back surface indicated at 43. The intersection of blade 33 with cylindrical hub 35 generates a section which, when developed on a plane surface, has the same shape as the section shown in FIGURE 2. Each section of blade 33 made by cylindrical surfaces at different radii from the axis of hub 35 will be a separate member of the family of hydrofoil sections of the modification of the present invention, as shown in FIGURE 2.

Propellers of the type shown in FZGURE 5 can take advantage of the high rotative speeds of marine gas and steam turbines, Without the attendant heavy reduction gears presently required, and open up the possibility of efficient propulsion at essentially unlimited speeds.

The supercavitating hydrofoil of the present invention, when used on hydrofoil boats, can extend the upper limit of speed of such boats to the point where it is limited only by the propulsion means. When it is incorporated in take olf and alighting gear for seaplanes, these can attain hydrodynamic performance comparable with aerodynamic performance.

As previously noted, the foil shape of the present inven tion is not limited in use to propellers or water borne craft but can be used in connection with other fluid dynamic devices and for other purposes. The same invention described herein can for instance be used in the construction of simple efiicient liquid pumps or turbines. Other applications will be readily apparent to those skilled in the art.

In connection with the foregoing, the term normal operation relates to supercavitating hydrofoils of the present invention which are so oriented to the direction of relative flow that the lower surface is entirely wetted by the flow and the upper surface lies entirely within the the cavitation envelope. Such required angles of orientation are well known to those skilled in the art.

The novel principles of this invention are broader than specific embodiments recited above. Accordingly, rather than unduly extend this disclosure by attempting to list all the numerous modifications that have been conceived and reduced to practice during this development, these novel features are defined in the following claims.

I claim:

1. A hydrofoil for efficient operation under supereav itating conditions comprising an upper surface, a lower surface, a sharp leading edge and a trailing edge both formed by the intersection of said upper and lower surfaces, said upper surface shaped so that in normal operation it is entirely within a cavitation envelope extending from said leading edge, and said lower surface being (a) entirely wetted in normal operation, (In) essentially of a curvature from the leading edge to the trailing edge following the general geometric e uation y"'(x) 0, wherein x is of a value from 0 to s and signifies the distance from the leading edge to a point lying on and measured along a base line drawn through the leading edge and parallel to the direction of the movement of the fluid relative to the hydrofoil, s is the distance from the leading edge to the intersection of the normal projection of the trailing edge on said base line, and y is the normal distance from the said base line to the said lower surface measured positive upwards, substantially all points along the lower surface from the leading edge to the intersection of said base line with the lower surface being above the base line, and (c) of a concave curvature adjacent the trailing edge, said last named concave curvature lying below the base line between said intersection and the trailing edge, the said lower surface thereby being so shaped as to in normal operation produce on the forward part thereof a net force in a direction opposite the direction of flow of the fluid relative to the hydrofoil which tends to compensate the pressure force on the after part of said lower surface in the direction of the fluid flow, thus tending to maximize the efiiciency of said hydrofoil.

2. A supercavitating hydrofoil as set forth in claim 1 wherein the curvature of said lower surface follows the geometric equation:

e) er en 8 511' E s 3 s 4 s where: j

x=the coordinate of the foil surface parallel to the direction of the movement of the fluid relative to the foil.

y =the coordinate of the foil surface normal to the x direction.

s=the body chord length of the foil.

C :the lift coeflicient of the foil defined as L goU s where:

L=lift U=relative velocity of fluid parallel to x axis =constant fluid density.

3. A supercavitating hydrofoil as claimed in claim 1 wherein said upper surface is convex.

4. A supercavitating marine propeller having hydrofoil blades as claimed in claim 1.

5. A liquid pump having supercavitating hydrofoil impellers as claimed in claim 1.

References Cited in the file of this patent UNITED STATES PATENTS 

